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Find the values of the constants $A$, $B$, and $C$ - Edexcel - A-Level Maths Pure - Question 3 - 2011 - Paper 5

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Find the values of the constants $A$, $B$, and $C$. $$\frac{9x^2}{(x-1)^2(2x+1)} = \frac{A}{(x-1)} + \frac{B}{(x-1)^2} + \frac{C}{(2x+1)}$$

Worked Solution & Example Answer:Find the values of the constants $A$, $B$, and $C$ - Edexcel - A-Level Maths Pure - Question 3 - 2011 - Paper 5

Step 1

Substituting $x = 1$

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Answer

To find the value of BB, substitute x=1x = 1: 9=3BB=39 = 3B \\ B = 3

Step 2

Substituting $x = -\frac{1}{2}$

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Answer

Next, substitute x=−12x = -\frac{1}{2}: 94=C(−12−1)2C=1\frac{9}{4} = C\left(-\frac{1}{2}-1\right)^{2} \\ C = 1

Step 3

Finding $A$

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Answer

Using the x2x^2 terms: 9=2.4A+C9=2.4A+1A=49 = 2.4A + C \\ 9 = 2.4A + 1 \\ A = 4

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